II is limited in this case. Therefore, Equations 52 and 54 from Ref. 15 are considered,δbeing the sheet thickness ratio (thinner/ thicker) and tu being the thinnest sheet thickness. Kre s = 0.1668 – 0.0097δ + 0.0302δ 2 + 0.1461δ 3 σbu++ t u Equation 54 from Ref. 15 The following analysis relies on three main assumptions: 1. Spot weld fracture occurs when the maximum load (CTS, proportional to the maximum nominal stress σbu ++) is reached, this assumption being supported by observations by Dancette et al. (Ref. 6). 2. Spot weld fracture occurs when a critical KI or Kres is reached, corresponding to the toughness of the spot weld nugget. 3. The critical KI or Kres is constant throughout the nugget independent of the welded configuration. Although, it is acknowledged that to consider the notch and thermal effects would imply distinguishing different critical KI or Kres depending on cooling rate or location inside the nugget. Based on these assumptions, the equations above can be written at the failure onset, both for similar and dissimilar configurations with the same minimum sheet thickness tu. Dividing one by the other yields the following expressions for the ratio between CTS for dissimilar and similar configurations, based on KI and Kres, respectively. These computed ratios can be directly compared with the average experimental ratios obtained from Table 4; all the data being plotted in the same graph — Fig. 10. Clearly, the order of magnitude of the mechanical effect, as computed through the elastic analysis from Ref. 15, appears very consistent with the experimental data. Further work by Dancette et al. (Ref. 16) also supports the evidence of a strong mechanical effect explaining the positive deviation. This study used finite element modeling to predict the failure of the TRIP800 spot welds presented here. In that study, two different numerical approaches are considered for failure prediction 1. Similar to the above analysis from Radaj and Zhang (Ref. 15), the onset of fracture is predicted through a critical fracture mechanics parameter, but in this case the J-integral, computed through finite element analysis. A critical J-integral level of 22.5 kJ/m² is found to be appropriate for the TRIP800 spot weld molten zone. This critical level is reached for a cross-tensile load of 3.3 kN in the case of a 5-mm-diameter weld in 1+1- mm configuration, and for a cross-tensile load of 5.1 kN in the case of a 5-mm-diameter weld in 1+2-mm configuration. These results in predicted CTS are fully consistent with the experimental results displayed in Fig. 3 (Ref. 16). 2. In a second part of their study, a cohesive zone model was used to predict the spot weld failure during cross-tension testing. Although the predicted CTS for the same configurations (5-mm-diameter weld, 3.86 kN in 1+1-mm similar configuration and 5.39 kN in dissimilar 1+2-mm configuration) are slightly high compared to the experimental results in Fig. 3, they are still in the range and their ratio is clearly consistent with the positive deviation effect. CTS CTS dis s imilar s imilar = 0.1668 – 0.0097 + 0.0302 + 0.1461 0.1668 – 0.0097δ + 0.0302δ 2 + 0.1461 3 from Equation 54 δ CTS CTS dis s imilar s imilar = 0.1012 + 0.0233 + 0.1615 + 0.0473 0.1012 + 0.0233δ + 0.1615δ 2 + 0.0473 3 from Equation 52 δ KI b = 0.1012 + 0.0233δ + 0.1615δ 2 + 0.0473δ 3 σ u ++ t u Equation 52 from Ref. 15 42 JANUARY 2014 Fig. 8 — Schematic view of the thermal, notch and mechanical effects for the main configurations. Fig. 9 — α as a function of the thickness ratio for two-sheet configurations. Fig. 10 — Comparison between CTS dissimilar and similar joint strengths as function of the thickness ratio for two-sheet configurations.
Welding Journal | January 2014
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